52

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17

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‘goeag PeOH YNOUITH PORTA PROH ITH

oUeTd “ALVZOuWAg yuey Ting - TROT AIOA 909770



NOTICE

The United States Government does not endorse products
or manufacturers. .Trade or manufacturers’ names appear
herein solely because they are considered essential to the
object of this report.

NOTICE

This document is disseminated under the sponsorship of
the Department of Transportation in the interest of
information exchange. The United States Government
assumes no liability for its contents or use thereof.


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FIGURE 6. DETAILED FINITE ELEMENT MODEL OF TRINITY CAR WITHOUT HEAD BRACE


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24

where da/dN is the fatigue crack growth rate, AK is the stress intensity factor range, and A and m are
material constants dependent on the environment, stress ratio, temperature and frequency (of the stress
excursions). The effects of stress ratio, or mean stress, are at least partially accounted for in the

following formulation, first proposed by Forman[12]

da _ A AK" (3)
aN 1-R

where R is the stress ratio, Sin/Sjyax- The crack growth constants A and m used in this analysis were
taken from values reported by Rolfe and Barsom[13] as lower bound values for pearlitic steels.
These are

A=3.8x 107°

m=3

The general relationship for the stress intensity factor range can be written as

AK = Y AS na 4)

where Y is a geometry dependent factor, AS is the stress range, and a is the crack length. The
solution for the stress intensity of a semi-elliptical crack in a plate was used in this analysis to model a
fatigue crack growing in Mode I through a plate member[14].

The estimated crack propagation life is strongly dependent on the assumed initial crack size.
An initial crack size of 0.25 inch was used for this analysis because it represents the lower limit of
what could reasonably be detected in the field[15]. Smaller assumed initial crack sizes would
have, of course, produced significantly increased crack growth life estimates. Larger assumed crack
sizes would have had the opposite effect. Since this study was done to identify the relative likelihood
of fatigue cracking at various sites at the stub sill/tank car interface, the selected initial crack size was
not a critical issue. This would not be the case in a situation where accurate estimates of remaining
life or safe inspection intervals were to be determined; initial crack sizes would have to be closely tied
to the reliability of the inspection system and well defined loading conditions.

Crack growth life at a specific location within the stub sill/tank car interface was defined as
the service interval within which a 0.25 inch crack would grow to a length of 1.00 inch. Only the

cracking sites most commonly seen in service were examined to evaluate relative crack growth lives.


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37

potentially critical stub sill locations are illustrated in Appendix A, where color plots of the Von Mises
stress contours are shown for each high stress location and loading combination.

The relative likelihood of fatigue crack initiation at each of these sites was again correlated
with the magnitude of the Von Mises (or octahedral shear) stresses reported in Table 7. As with the
NATX car, those locations showing Von Mises stresses in excess of the cyclic yield strength for these
materials could be expected to initiate fatigue cracks after relatively few of these high loadings
(hundreds to thousands of cycles). Locations showing lower Von Mises stresses may also eventually
develop fatigue cracks, but the likelihood of their occurrence would depend on the nature and severity
of the actual service spectrum.

The highest computed Von Mises stresses for the Trinity car for each type of loading are
summarized in Table 8. Whether the tank was full or empty and whether a head brace was included
or not is also identified. The computed Von Mises stress values are ranked separately for each loading
condition, because the criticality of these sites in terms of fatigue crack initiation depends directly on
the relative frequency of occurrence of these different types of loading. As stated earlier in the NATX
tank car discussion, the first two loading conditions are commonly withstood by tank cars in normal
service (at varying severity levels), while the last two loading conditions are not. However, the
concer with the offset vertical loading is not so much the introduction of fatigue cracks, as it is the
possibility of substantially and permanently deforming the tank car, especially a full tank car without
head braces.

3.2.2 Potentially Dangerous Cracks

The sites of potentially dangerous cracks in the Trinity car were identified by examining the
locations where the highest Von Mises stresses were identified (as in Table 8), comparing these
locations with sites (and planes) where cracks have been most frequently observed in the field, and
then assessing the potential for Mode I crack growth in these potentially critical cracking planes. In
order to do this it was necessary (as done earlier for the NATX car) to identify the principal stress
components at each of the sites identified in Appendix A. A variety of other cases showing relatively
high stress levels orthogonal to the commonly observed cracking planes were also examined. These
results are compiled in Table 9 and are shown in Appendix B. Where two stress components are

shown for the same location and stress direction, they represent values at two different potentially


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1.0 INTRODUCTION

Stub sill tank cars are used to carry a variety of liquid chemicals and products. Many of these
substances are considered hazardous. The safe transport of these materials depends to a large extent
on tank car structural integrity. In a stub sill tank car, the tank is the main load carrying structural
member with short (stub) sills at each end to attach the wheel truck and coupler. The stub sill - tank
shell region is an area of particular concern because of the significant fluctuating stresses and the
consequent potential for fatigue cracking and subsequent leakage.

Cracks in the tank car shell or weldment can develop from fatigue, corrosion or other causes.
Service, maintenance, inspection, or derailment loads will induce stresses of various magnitudes and
directions in the structure. Tensile stresses resulting from these loading conditions that are normal to
any of these cracks will tend to open and propagate them.

The likelihood of fatigue cracking at potentially critical locations in two different stub sill tank
car designs was evaluated in this study:

. North American Car Company, NATX 34081 Series, 33,800 gallon capacity, and

. Trinity Industries TK-S Class, DOT-111A100W1, 26,000 gallon capacity.

Figures 1 and 2 show overall views of the NATX and Trinity car finite element models.

The NATX car analysis was completed first because Battelle had done a previous study on this
car, and drawings were immediately available{1]". The Trinity car was also chosen for analysis
because the Federal Railroad Administration and the Volpe National Transportation Systems Center
(VNTSC) had a testing program underway at the Transportation Test Center (TTC) using a Trinity
car[2]. As a result, the finite element results could be used as a supplement to their test data. In
addition, correlation of the two provided a good validation of the analytical results.

The objectives of this study were to:

1) perform a detailed stress analysis of existing stub sill tank cars,
2) evaluate the stub sill inspection procedure,

3) evaluate service/design loads, and

4) characterize stresses for service life prediction.

The ten load cases chosen for this study are summarized in Table 1. The compression buff
and upward vertical load cases represent common service loads. The pure torsion loading case was

used to simulate the loading that might occur in a rollover derailment of a stub sill tank car. The

References are listed on page 67.


Figure

A Peis =

13.
14.
15,
16.
17.
18.

19.
20.

21.

22.

23.

25.

26.

LIST OF ILLUSTRATIONS

FINITE ELEMENT MODEL FOR THE NATX 34081 SERIES CAR .............--
FINITE ELEMENT MODEL FOR THE TRINITY CAR, CLASS TK-S
DETAILED FINITE ELEMENT MODEL OF NATX CAR WITH HEAD BRACE ......
DETAILED FINITE ELEMENT MODEL OF NATX CAR WITHOUT HEAD BRACE ..
DETAILED FINITE ELEMENT MODEL OF TRINITY CAR WITH HEAD BRACE ....
DETAILED FINITE ELEMENT MODEL OF TRINITY CAR WITHOUT HEAD

BRAGE sas sare os wok Wey Oe Cae ele WOU Wola EW RUM He HOU NER Kale eae mE ROS 8
VNTSC SHELL PROGRAM RESULTS FOR THE NATX CAR IN COMPARISON

WITH FINITE ELEMENT RESULTS

QUARTER SYMMETRIC MODEL . . E E « 12
HALE'SYMMETRIGC MODEL |. oeie snes cowie: tunis cae asin siete bine iele severe ie boone: axe 13
COMPRESSION BUFF LOADS AND BOUNDARY CONDITIONS .............-- 14
UPWARD VERTICAL LOAD AND BOUNDARY CONDITIONS ...............-- 15
OFFSET VERTICAL (INSPECTION PROCEDURE) LOAD AND BOUNDARY
CONDITIONS "EMPTY TANK. sie isco s:asersicunre Wale sale HON SOS KEG eR Rae's Sais He 16
OFFSET VERTICAL (INSPECTION PROCEDURE) LOAD AND BOUNDARY
CONDITIONS = FUEL TANK siaseissieie oss axew arate scaa sere sews stare vireo axes arate ois 17
PURE TORSION (ROLLOVER DERAILMENT) LOAD AND BOUNDARY

CONDIBIONS \. scsie esos vneys Sheraceatieywoalls, Gece eawte.enuade wale) wena sues dace ey atanenanele wlele: ene 18
EXAGGERATED DISPLACEMENT PLOT OF NATX CAR - COMPRESSION BUFF

LOAD Fieri) siloe 2 sGialec sists ete? eae elven elise ee are STS 20
AAR DESIGNATED CRITICAL AREAS . ‘ 32
ADDITIONAL AREAS OF OBSERVED CRACKING 33
GENERAL VIEW OF STRAIN GAGED AREA ADJACENT TO THE STUB SILL ON

THE TRINITY CAR. wos: isc wis saawaiew mete nen was Saw TE smaes Bae Wate ate wes oe 42
CLOSEUP VIEW OF STRAIN GAGED AREA ON THE TRINITY CAR ........... 43
ILLUSTRATION OF EQUIVALENT UPWARD VERTICAL MOMENTS APPLIED IN

THE FIELD. AND IN THE ANALYSIS a. cia no soe go ga sis wars wweiaces HH oes 45
LONGITUDINAL STRAIN CONTOURS IN THE STRAIN GAGED AREA FOR

THE UPWARD VERTICAL LOADING CASE ces. coe cesses sini wine wrateieievere obaie oie 48
CIRCUMFERENTIAL STRAIN CONTOURS IN THE STRAIN GAGED AREA FOR

THE UPWARD VERTICAL LOADING CASE ....... 0.0... 00 ce eee eee eee 49
LONGITUDINAL STRESS CONTOURS IN THE STRAIN GAGED AREA FOR

THE UPWARD VERTICAL LOADING CASE ............ 0. ccc cece cence eens 51
CIRCUMFERENTIAL STRESS CONTOURS IN THE STRAIN GAGED AREA FOR

THE UPWARD VERTICAL LOADING CASE 2:3. 06%. 000 60's oe sine Soe eeiee cee oe 52
MAXIMUM PRINCIPAL STRESS CONTOURS IN THE STRAIN GAGED AREA FOR
THE UPWARD VERTICAL LOADING CASE ..... 0.600 ec ccc cee ceeaeeceees 53

MINIMUM PRINCIPAL STRESS CONTOURS IN THE STRAIN GAGED AREA FOR
THE UPWARD VERTICAL LOADING CASE .... 0.6.0.0 600 e cece cece eee eee 34


34

area, especially if large coupler draft loads were experienced with regularity. In this case, cracking
across the Z-section (vertically) would be expected.

If fatigue cracks were already present in a tank car that was subjected to an offset vertical
loading, further damage could be incurred, especially in the Z-section lug area and the transition plate.
If significant cracks were present in the tank shell when a large offset vertical load was applied,
further damage could also result, especially if there was no head brace installed. However, further
damage from an offset vertical loading could be incurred in a cracked transition plate of an NATX
tank car, even if a head brace were installed.

3.2 Trinity Car Class TK-S, ATSF 98600-94749

After the NATX tank car analysis was completed, a similar study of a Trinity car, class TK-S,
was undertaken. The following paragraphs provide a summary of the findings from that analysis. The
sites of greatest crack initiation potential are reviewed first, and then the locations of potentially

dangerous fatigue cracking are identified.

3.2.1 Crack Initiation Potentials

A summary of the maximum Von Mises stresses for potentially critical stub sill locations in
the Trinity Tank Car, Class TK-S, ATSF 98600-94749, is included in Table 7. As with the NATX car
analysis, this table was constructed to allow simple comparisons between the maximum Von Mises
stresses in various components as a function of tank condition. The substantial increase in maximum
stress levels between the empty and full condition seen for the NATX car for the offset vertical
loading case was also apparent in the Trinity car analysis. The maximum Von Mises stresses were
also considerably higher in almost all cases for the Trinity tank car without the head brace installed
than with it in place. There are a few minor exceptions such as in the tank shell for the offset vertical
loading and in the rear draft lug area for the compression buff loading, where the introduction of a
head brace actually increased stresses slightly.

Of the four load cases considered, the offset vertical loading produced the highest stresses at
most locations in the stub sill/tank car interface area (as seen earlier with the NATX tank car). The


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FINAL REPORT

TECHNICAL TASK DIRECTIVE NO. VA-1039
CONTRACT NO. DTRS-57-89-D-00006

on

STRESS ANALYSIS OF STUB SILL TANK CARS

to

VOLPE NATIONAL TRANSPORTATION SYSTEMS CENTER
RESEARCH AND SPECIAL PROGRAMS ADMINISTRATION
U.S. DEPARTMENT OF TRANSPORTATION

December 15, 1993

by

Charles R. Miele and Richard C. Rice

Battelle
505 King Ave
Columbus, Ohio 43201


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TABLE OF CONTENTS

Section Page
1.0 INTRODUCTION ssiis oss sass sine swe aise Rieiee ale SSG & Hale HOE OSE RSH NOT EWG Soe weiee 1
2:0 ANALYSIS PROCEDURE) ioc. wise ssscs wan wiais wate vias vate 8a Ris ERG ERY Wow HA ERO 9

2.1 Mesh Generation and Modeling Assumptions ........ ore an 2

2.1.1 Model Validation and Quality Assurance . see 5 E
2.2 Load Applications and Boundary Conditions ...... a8 - 10
2.3 Stress Analysis :

2.4 Assumed Field Loading Spectra 21
2.5 Crack Initiation Analysis Methodology .............. 00 cece eee ee ee eeeeee 22
2.6 Crack Growth Analysis Methodology ............ 00.002 ce eee eee eeeeee 23

3.0 Evaluation of Cracking Potential and Criticality See 25

3.1 North American Tank Car; NATX 34081 Series ... 25

3.1.1 Crack Initiation Potentials ............ - -. 26

3.1.2 Potentially Dangerous Cracks ....... 0... cece cece eee 29

3.2 Trinity Car Class TK-S, ATSF 98600-94749 2.0... 2. eee ee eee eee 34

3.2.1 Crack Initiation Potentials .... . é .. 34

3.2.2 Potentially Dangerous Cracks 37

4.0 Evaluation of Stub Sill Inspection Procedure ...........-... 000 cece cece cece eee 39

5.0 Correlation of Analytical and Experimental Results ...............00002eeeeeeeeee 41

6.0, Discussion of Resulltg, u.. ..10 ince ware sess suare ane ware wiavione wae suaite esse WLU Wwe GH elatei & 59

6.1 Crack Initiation Potentials ..... 59

6.2 Potentially Dangerous Cracks . . 64

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BLO; References) wes see merece ace ale sie soe Bee WOR MULE Sale RAW Kee TSS WAN ES FES Ha 67
APPENDICES

A Von Mises Plots for Potentially Critical Locations ...........0....00 eee eeeeeeeees A-l

B Local Stress Plots for Each Potentially Critical Location ................ 0c ee eeeeeee B-1

C Stress Plots Supporting the Stub Sill Inspection Procedure ..............-..-2-000000- C1

iv


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22

vertical loads (with shelf couplers) as high as 50,000 Ibs. The AAR Specifications for Design,
Fabrication and Construction of Freight Cars[6] also call out these load levels as limits that
must be withstood without "yielding the loaded members or exceeding their critical buckling
strengths". Each of these spectra were assumed to act independently for this analysis, with the

possibility of simultaneous high loadings considered to be remote.

2.5 Crack Initiation Analysis Methodology

Fatigue cracks generally initiate at a geometric discontinuity such as a notch or weld toe.
These act as stress concentrations, magnifying the stresses in this region to levels above the nominal
levels. Subjecting these regions to cyclic loading may cause repeated plastic deformation that will
eventually result in one or more fatigue cracks. Although a reasonably detailed finite element mesh
was used in the stub sill/tank interface, the mesh was not fine enough to provide truly accurate
estimates of the local stresses at points of highest stress concentration. Therefore, the fatigue
calculations included here should be used as a relative measure of the likelihood of fatigue cracking in
various locations as a result of the various assumed loadings. Avoidance of fatigue cracking in actual
practice with these stub sill designs should be based on a detailed examination of the severity and
integrity of the geometric details in the areas of highest predicted stresses, combined with a careful
assessment of the actual vehicle loadings. The fatigue calculations that are presented in the following
paragraphs should be viewed with these caveats in mind.

Low cycle fatigue strain-life data are often represented by the Coffin-Manson[7] equation,
with Morrow’s[8] mean stress correction factor as follows:

A  , Op - om) 1
SE = el any + ——TM ny? @

where Ae/2 is the strain amplitude, €’; is the fatigue ductility coefficient, 0’, is the fatigue strength
coefficient, ,, is the mean stress, 2N; is the reversals to failure, c is the fatigue ductility exponent, and
b is the fatigue strength exponent. By relating the strain calculated at the notch root to the strain-life
data, the number of cycles to initiate a fatigue crack at the notch can be estimated. This is the basis of
the initiation life predictions. The strain-life data parameters, €’;, 0’;, c, and b, are obtained either by


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46

Table 10a shows finite element predicted strains compared with measured strains for the
vertical coupler force case. Figures 21 and 22 provide color contour plots of the finite element
analysis strains in the longitudinal and circumferential directions.

The stress/strain gradients were fairly high in this area relative to the element sizes. This need
for interpretation of the contour plots led to some uncertainty in the comparison with test results. The
stress value at a specific location was estimated by interpolation within the contour lines.

There were some discrepancies side-to-side in some of the experimental strain readings from
symmetric load cases. The strain gages were probably not placed exactly symmetrically from one side
to the other. The high strain gradients in this area, especially near the tank/sill intersection, may also
have contributed to the differences in side-to-side strain readings. Also, conversations with David
Cackovic at TTC revealed that some of the strain-gaged cars had cracks or developed cracks during
some of the tests[15].

Table 10. Comparison of TTC Strain Gage Results with Battelle Finite Element Analysis
Results

(a) Strain results comparison - Vertical Coupler Force/Upward Vertical Load

Strain Components Strain Gage No. Test (y Strain) FEA (, Strain)
25/31 -391 to -439 -482 to -750
“tong 48 -98 -135 to -482
48 -50 0 to -135
8/28 -180 to -232 -205 to -344
& 27133 -227 to -346 -400 to -700
ont 47 -216 -100 to -360
50 -140 0 to -100
10/30 -52 -17 to -187



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41

If significant cracks were present in any of the regions exposed to these high stresses, the
acoustic emission procedure would likely be sensitive to them. This would be especially true if the
maximum principal stresses in these regions tended to open up these cracks. Because the regions of
highest stress resulting from the offset vertical loading most closely parallel the regions of maximum
stress resulting from the upward vertical loading, it appears likely that the inspection procedure would
be more sensitive to cracks caused by upward vertical service loadings than cracks caused by
compression buff service loadings.

There is some risk of damage to either of these tank cars from the inspection procedure,
especially if the procedure is performed on cars with no head brace and a full tank. For this condition
the local stresses are likely to be so high that significant, permanent deformation (or even failure) of
the tank car could occur. The likelihood of damage would be reduced if the load could be applied
incrementally, while listening for acoustic emissions at each load step. If significant acoustic

emissions are heard, a careful inspection of the tank car should be made before increasing the load
further.

5.0 CORRELATION OF ANALYTICAL AND EXPERIMENTAL RESULTS

Two of the Trinity Tank car test cases run at TTC were found to be equivalent to two of the
finite element analysis cases. The "Longitudinal Coupler Force" test was equivalent to the
"Compression Buff Load" analysis case, and the "Vertical Coupler Force" test was equivalent to the
“Upward Vertical" analysis case. Both were performed with a full tank on a tank car without a head
brace.

The strain gage data came from several sets of strain gages that were placed near the
termination of the sill-to-tank weld near the tank-head on the end of the tank car with no head brace,
as shown in Figures 18 and 19. Some of the strain gage locations were duplicated symmetrically left
to right. This is evident in Figure 19 at those sites showing two gage ID’s with the suffixes "L" or
"R". Figure 18 shows the general area on the tank car where these strain gages were located. Figure
19 is a close-up of this area showing the strain gage numbers and their orientations. Note that this
figure shows only the orthogonal gages referenced in this comparison.

Since there were only stress results available for the Compression Buff load finite element

analysis, comparisons with test data were made in terms of stress for this load case. For the Upward


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FIGURE B-41. TRINITY Z SECTION LUG AREA, VERTICAL STRESS, COMPRESSION BUFF LOAD, FULL TANK, NO
HEAD BRACE (SECOND VIEW); Maximum Stress


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PREFACE

This report summarizes the results of a detailed stress analysis and fatigue assessment of two
stub sill tank car designs often used for the transport of hazardous materials. This particular class of
railroad cars has come under scrutiny by the Federal Railroad Administration in recent years because
of occasional stub sill tank car failures that have led to the release of hazardous materials. The United
States and Canadian governments asked the tank car industry to inspect at least 1,100 tank cars,
perform a theoretical analysis of the stub sill problem, and then evaluate the inspection results
compared with theoretical calculations.

In line with these actions, the FRA decided that an independent, detailed stress analysis of
several common stub sill tank car designs was needed to assist in the determination of whether certain
corrective actions taken by the industry would help reduce the incidence of stub sill fatigue cracking
and to help the parties involved evaluate the criticality of cracks found during routine inspections.

The shell of a stub sill tank car is a primary structural element, since any buff or draft forces
incurred in service are transmitted through the tank shell. The most critical site, in terms of stress
concentration and the likelihood of fatigue cracking, tends to be the welded region where the stub sill
is welded to the tank shell. That stub sill/tank shell transition region was the primary focus of the
study described in this report.

This work was sponsored by the FRA Office of Research and Development in Washington,
D.C. under the guidance of Mr. Jose Pena. The technical effort was monitored by the Volpe National
Transportation Systems Center (VNTSC) in Cambridge, MA. The key individuals at VNTSC were
Ms. Yim Har Tang and Dr. Oscar Orringer. The ongoing technical reviews and guidance provided by
these individuals is gratefully acknowledged by the authors.

An integral part of this study was the comparison of stress analysis predictions with actual test
results on a strain-gaged stub sill tank car tested at the Transportation Test Center in Pueblo, CO. The
cooperation and assistance of Mr. David Cackovic of TTC is very much appreciated.


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44

Vertical load case, comparisons were made wherever possible in terms of both stress and strain.

Data from the laterally and longitudinally oriented strain gages were multiplied by Young’s
modulus (30,000,000 psi) to convert them to stress values, and then compared with the finite element
stress results in the lateral and longitudinal directions relative to the model’s local "elemental"
coordinate system. Maximum and minimum principal stresses were calculated from the strain data and
from the finite element analysis results to provide an additional comparison.

The load magnitudes used in the tests were not exactly the same as the loads used in the
corresponding finite element analysis load cases. The maximum "Longitudinal Coupler Force" (LCF)
load used in the test was 324,500 Ibs. The "Compression Buff Load" applied in the corresponding
finite element analysis case was 350,000 Ibs. Finite element analysis stress results were scaled to
provide a direct comparison with test results. For example, the stress results from the compression
buff load case finite element analysis would have to be multiplied by 0.926 before comparing them
with the stresses calculated from the test results.

The maximum "Vertical Coupler Force" (VCF) used in the test was 20,100 Ibs applied where
the car couplers meet - 15.75 inches away from the striker plate. The "Upward Vertical" load in the
finite element analysis case was 50,000 Ibs applied at the striker plate. This means that the loading
used in the finite element analysis was substantially different from the loading used in the test. When
compared directly, one is a force, and one is a force plus a moment, so the results could not be scaled
exactly for comparison. However, the area of comparison (strain gaged area) is relatively far from the
load application point, so the results could be approximately scaled by converting the loads to
moments about the truck center line and scaling to their ratio. Figure 20 shows a simple diagram of
the equivalence calculations. This method yielded a scale factor of about 2.

To ensure an accurate comparison, a new “Upward Vertical" finite element analysis case was
run using the same load and moment arm as in the test. Both stresses and strains were recovered in
this new analysis and compared with the test results.

The orthogonal strains were compared at four locations. The finite element analysis strain
results predicted higher strains than those found experimentally in the areas of highest stress (SC 30-
32). The comparison was closer in other areas. In general, the strains predicted by the finite element
analysis were always the same sign as the strains from the test results, and their magnitudes were in

the same range.


APPENDIX C

Stress Plots Supporting the Stub Sill Inspection Procedure


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26

3.1.1 Crack Initiation Potentials

A summary of the maximum Von Mises stresses for potentially critical stub sill locations in
the North American Tank Car, NATX 34081 Series, is included in Table 4. This table was
constructed to allow simple comparisons between the maximum Von Mises stresses in various
components as a function of tank condition (i.e. tank full or empty, head brace installed or absent).
The dramatic (and anticipated) increase in the maximum stress levels between the empty and full
condition is also apparent at all locations for the offset vertical load case (the only one considered for
both empty and full tank conditions in this study). Similarly, the maximum Von Mises stresses were
considerably higher in almost all cases for the NATX tank car without the head brace installed than
with it in place. There are a few minor exceptions, such as in the Z-section lug area and weld for the
compression buff loading, where the introduction of a head brace actually increased stresses slightly.

Of the four load cases considered, the offset vertical loading produced the highest stresses at
most locations in the stub sill/tank car interface area. In fact, for the full tank/no head brace condition
some of the computed (linear elastic) stresses far exceeded 80,000 psi, suggesting the possibility of
significant inelastic deformation resulting from this tank and loading combination. Table 4[17].
summarizes the relative comparisons between various load cases (with and without head braces) for
the various critical locations.

The potentially critical stub sill locations are illustrated in Appendix A. Color plots of the
Von Mises stress contours are shown for the high stress locations and loading combinations in
appendix A. Note that appendix A does not directly correspond to each location/case in table 4
because appendix A shows only the locations of high or significant stresses. Table A-1 summarizes
the locations of those high stresses.

The relative likelihood of fatigue crack initiation at each of these sites can be correlated, at
least approximately, with the magnitude of the Von Mises (or octahedral shear) stresses reported in
Table 4. Although the detailed calculations are not presented here because the results of this study are
meant to be interpreted qualitatively, it can be said that those locations showing Von Mises stresses in
excess of the cyclic yield strength for these materials (roughly 50 to 70 ksi) could be expected to
initiate fatigue cracks after relatively few of these high loadings (hundreds to thousands of cycles).
Locations showing lower Von Mises stresses may also eventually develop fatigue cracks, but the
likelihood of their occurrence would depend on the nature and severity of the actual service spectrum.

The focus of the crack growth analysis is on the most severe sites depicted in Appendix A.


51

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Associated Morkeet: 1-WoRRING S72

= -61.9 ksi

FIGURE B-46. TRINITY HEAD PAD, LONGITUDINAL STRESS, UPWARD VERTICAL LOAD, FULL TANK, NO HEAD
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LIST OF ABBREVIATIONS AND SYMBOLS (Continued)

Longitudinal stress
Mean stress
Maximum stress
Minimum stress
Nominal stress
Longitudinal stress
Cyclic yield strength

ix


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10
2.1.1 Model Validation and Quality Assurance

The finite element models of both the NATX and the Trinity Car were checked for validity
and accuracy in several ways. The weight of the car components that were listed on the engineering
drawings were compared with the weight that the finite element program calculated.

Weld locations and plate thicknesses in the finite element model were independently checked
at Battelle by a knowledgeable person other than the person who built the finite element model. Plots
of the weld locations were routed through VNTSC to the Trinity Car Co. and to the North American
Car Co. for further confirmation. Sketches of loading and boundary conditions as understood by
Battelle were sent to VNTSC to confirm that these conditions were represented properly. Exaggerated
deformation plots were produced for each load case to confirm that the structure was reacting
realistically to the applied loadings.

Finite element analysis stress results along the bottom of the tank shell from the Compression
Buff load case were compared with a closed-form shell-theory analytical solution developed by
VNTSC. A comparison of finite element results with the output from the shell program is shown in
Figure 7. The results of the finite element analysis agreed with the VNTSC shell theory results within
about 14 percent near the load application point, and within 10 percent in areas away from the load
application point. The purpose of this comparison was not to achieve exact correlation; it was done to

provide a reasonability check for the finite element calculations.

2.2 Load Applications and Boundary Conditions

There were two different boundary conditions used, depending on load symmetry. The
"Quarter-Symmetric" load cases were the Compression Buff load and the Upward Vertical load. The
“Half-Symmetric" load cases were the Offset Vertical load cases (as used in the acoustic emission
inspections) with Full Tank and Empty Tank, and the Pure Torsion load case (simulating loading that
might occur in a tank car derailment). Figure 8 shows a quarter symmetric model, and Figure 9 shows
a half symmetric model.

There were a total of ten load cases which represented a combination of full tank/empty tank,
and head brace/no head brace configurations (as detailed earlier in Table 1). Figures 10 through 14

are illustrations of the loading conditions shown on the NATX car. The loading conditions were the


39

Based on this analysis, full Trinity tank cars without head braces show the greatest potential
for dangerous service cracks in the Z section lug area. Longitudinal coupler loads would be the
primary contributor. Cracking across the lug appears most likely (if buff and draft loads of
approximately equal magnitude are experienced). However, large buff loads could also contribute to
the growth of longitudinally oriented cracks in the Z section lug area.

Full Trinity tank cars with head braces installed are also susceptible to the development of
dangerous service cracks. The analysis suggests that the most likely site remains the Z-section lug
area. Assuming that the stresses due to a draft load are opposite in sign to the stresses from the
compression buff load, cracking in the draft lug itself could occur if large coupler draft loads were
experienced with regularity.

If fatigue cracks were already present in a tank car that was subjected to an offset vertical
loading, further damage could be incurred in the Z-section lug area and the head pad. If significant
cracks were present in the tank shell when a large offset vertical load was applied, further damage
could also result. For the Trinity car, the presence or absence of a head brace has little impact on the
likelihood of further tank shell cracking due to an offset vertical loading.

4.0 EVALUATION OF STUB SILL INSPECTION PROCEDURE

The inspection procedure, also known as the "acoustic emissions” test, is done by attaching a
rigid 36" bar to the sill at the coupler end and lifting the end of the bar until one of the car’s wheels
lifts off the track a specified height. (The force required to lift the car during the inspection procedure
has not been measured.) During this jacking operation, the inspector listens for acoustic emissions to
isolate cracking locations. This loading was called the "Offset Vertical" load case in this study. (See
Figure 12 for an illustration of this load case).

The maximum computed stresses at the stub sill/tank car interface were quite high for the
offset vertical load case applied to a full tank (for both the NATX and Trinity Cars), particularly
when a head brace was not included in the model. Appendix C shows the Von Mises and Maximum
principal stress contours from various views for both the NATX and the Trinity tank cars under the
Offset Vertical (Acoustic Emissions Test) loading. These stress contours are shown for the full tank

car condition, with and without head braces.




B-43

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LIST OF ILLUSTRATIONS (Continued)

Page
LONGITUDINAL STRESS CONTOURS IN THE STRAIN GAGED AREA FOR
THE COMPRESSION BUFF LOADING CASE .........0. 00 e0eeceeeeeeeeees 55
CIRCUMFERENTIAL STRESS CONTOURS IN THE STRAIN GAGED AREA FOR
THE COMPRESSION BUFF LOADING CASE .........0-00-0eeceeeeeeeeee 56
MAXIMUM PRINCIPAL STRESS CONTOURS IN THE STRAIN GAGED AREA FOR
THE COMPRESSION BUFF LOADING CASE .........0. 00-0 eee eeeeeeeeeee 57
MINIMUM PRINCIPAL STRESS CONTOURS IN THE STRAIN GAGED AREA FOR
THE COMPRESSION BUFF LOADING CASE ........-00. 00-0 eeceeeeee cence 58

VON MISES STRESS CONTOURS - NATX CAR WITH HEAD BRACE .....
VON MISES STRESS CONTOURS - NATX CAR WITHOUT HEAD BRACE . .
VON MISES STRESS CONTOURS - TRINITY CAR WITH HEAD BRACE ...
VON MISES STRESS CONTOURS - TRINITY CAR WITHOUT HEAD BRACE

vi


sone TOONS VE Putin A doable

B-34

= -9.9 ksi

= 7.8 ksi, Minimum Stress

FIGURE B-34. TRINITY Z SECTION LUG AREA, VERTICAL STRESS, COMPRESSION BUFF LOAD, FULL TANK, WITH
HEAD BRACE (SECOND VIEW); Maximum Stress


19

same on the Trinity car except for the different magnitudes, as indicated.

Detailed stress results were produced for all the loading conditions described earlier. In
general, they showed the beneficial effect of adding a head brace on a fully loaded or empty car, as
well as a relative comparison, car to car, of a rollover derailment. It should be noted that the
magnitude of the pure torsion moment that was stipulated for these analyses was an arbitrary "unit
load" of 10,000 ft-lbs. Based on simple statics hand calculations, about 800,000 ft-lbs of pure torsion
at the coupler would be required to lift all the wheels on one side of a tank car off the rail. In reality,
this much torque on one coupler would cause plastic deformation and probably lead to stub sill
fracture. In a linear elastic analysis, this extreme load magnitude would result in unrealistically high
stresses (millions of psi), so the "unit load" was used for relative comparisons. Within the limits of
this linear elastic analysis, larger moments could be expected to produce proportionately larger stresses
in areas of concern.

The offset vertical loading does not represent a field service loading. It represents the loading
applied during occasional nondestructive inspections of selected tank cars. The test is done by
attaching a 3-foot-long rigid bar near the coupler end of the draft sill and raising the end of the bar
with a jack until one wheel just lifts off the rail. The jacking force magnitude has never been
measured. The load given to us by VNTSC for the acoustic emissions test inspection procedure load
case was based on their estimate of the force required to lift one wheel off the rail.

2.3 Stress Analysis

The SDRC I-DEAS program was used for all finite element analyses. This software package
was used for all pre-processing, solving, and post-processing. All analyses were static and linear
elastic.

Continuity across the solid/shell interface was checked by plotting the deformations for the
entire model and checking the deformation continuity. (Figure 15 includes a plot of the deformations
in this area for the Compression Buff load). The nearly continuous deformation lines on this plot
indicate reasonable load transfer. However, because of the mesh discontinuity between the solid and
shell elements, the stresses local to this discontinuity are not valid.

At the beginning of this project VNTSC suggested that Battelle assume the lading to be liquid
propane. This lading produced typical, but not "worst case" tank car loads, since liquid propane has a


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29

The highest computed Von Mises stresses for each type of loading are summarized in Table 5.
Whether the tank was full or empty, and whether a head brace was included or not is also identified.
The computed Von Mises stress values are ranked separately for each loading condition, because the
criticality of these sites in terms of fatigue crack initiation depends directly on the relative frequency
of occurrence of these different types of loading. The first two loading conditions are commonly
withstood by tank cars in normal service (at varying severity levels), while the last two loading
conditions are not. However, the concer with the offset vertical loading is not so much the
introduction of fatigue cracks, as it is the possibility of substantially and permanently deforming the
tank car structure. Stresses above the yield strength of the material were calculated in several areas for
the case of a full tank car without a head brace.

3.1.2 Potentially Dangerous Cracks

The sites of potentially dangerous cracks were identified by examining the locations where the
highest Von Mises stresses were identified (as in Table 5), comparing these locations with sites (and
planes) where cracks have been most frequently observed in the field, and then assessing the potential
for Mode I crack growth in these potentially critical cracking planes. In order to do this it was
necessary to identify the principal stress components at each of the sites identified in Appendix A. A
variety of other cases showing relatively high stress levels orthogonal to the commonly observed
cracking planes were also examined. These results are compiled in Table 6 and shown in Appendix B.
Where two stress components are shown for the same location and stress direction, they represent
values at two different potentially critical sites within the component.

For stub sill tank cars like the NATX and Trinity models described in this report the AAR has
designated three critical areas as shown in Figure 16. Cracking has also been observed in three other
areas as shown in Figure 17. Both of these figures illustrate potentially critical cracking sites for stub
sill tank cars with head braces installed. These figures illustrate the point that head braces do not
entirely eliminate the potential of fatigue cracking for all load cases, even though they significantly
reduce the potential of fatigue cracking for most loadings, as discussed elsewhere in this Teport.

Based on this analysis, full NATX tank cars without head braces show the greatest potential
for dangerous service cracks in the transition plate, near the end of the weld joining it to the tank

body. Longitudinal coupler loads would be the primary contributor. If draft and buff loads of equal


50

Figures 23 through 30 include stress and strain contour plots from the finite element analysis
for the strain gaged area under comparison. The stress values used for the comparison with test data
were estimated near the center of the element located closest to the corresponding strain gage set.
Each contour color band represents a variation in stress of at least 4,000 psi, and occasionally a
variation as high as 10,000 psi.

Tables 10b and 10c show the comparison of TTC’s strain gage data (converted to stress) with
Battelle’s finite element stress analysis results for the Vertical Coupler Force and Longitudinal Coupler
Force load cases. Figures 23 and 24 are color contour plots of the finite element analysis stress results
in the longitudinal and circumferential directions for the Upward Vertical load case. Figures 25 and
26 are color contour plots of the maximum and minimum principal stresses for the Upward Vertical
load case. Figures 27 and 28 are color contour plots of the finite element analysis stress results in the
longitudinal and circumferential directions for the Compression Buff load case. Figures 29 and 30 are
color contour plots of the maximum and minimum principal stresses for the Compression Buff load
case.

The experimental and analytical results agree fairly well in most locations considering all the
uncertainties inherent in this kind of comparison. The finite-element-calculated stress values in the
table can be interpreted within a tolerance of about 5 ksi. In general, the comparison of "Vertical
Coupler Force" to "Upward Vertical Load" and "Longitudinal Coupler Force" to "Compression Buff
Load" are within expected tolerances.

This level of agreement says that this model can be used to predict nominal stress levels in the
tank car structure. This model does not precisely account for the effect of highly local stress
concentrations such as in the vicinity of welds, bolts, and valves, since local geometric variations and
design anomolies substantially affect the severity of local stresses. However, this model can be used
to make meaningful qualitative comparisons between different design features and can also be used to

help select strain gage locations for other detailed experimental studies.


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low cycle fatigue testing or by using estimates.

Hardness measurements are often used to estimate fatigue properties of weldments in place of

mechanical testing to determine properties. Since fatigue cracks often initiate in the relatively narrow
metallurgical region of the heat affected zone (HAZ), direct testing is difficult. These estimated
material fatigue properties were obtained from an earlier Battelle study[1]. The significant parameters

are summarized in Table 3.

The fatigue properties for the weld bead were used for crack initiation fatigue life estimates
within a specific weld or within the weld’s HAZ. The fatigue properties for the sill pad extension

were used for crack initiation fatigue life estimates at locations away from welds.

Table 3. Estimated Fatigue Properties From Reference [1]

Identification Weld Bead Sill Pad Extension
Material TC-128B A515-70
Source GEIS] presacral
Material Properties
Ultimate Strength, Sy, ksi 127 85
Cyclic Yield Strength, o’,, ksi 71 52
Fatigue Strength Coefficient, 0’, ksi 174 134
Fatigue Strength Exponent, b -0.083 -0.094
Fatigue Ductility Coefficient, ©’, 0.72 0.89
Fatigue Ductility Exponent, c -0.6 -0.6
Cyclic Strength Coefficient, K, ksi 182 137
Cyclic Strain Hardening Exponent, 1’ 0.138 0.157

2.6 Crack Growth Analysis Methodology

For cases involving only localized yielding, it was shown over 30 years ago[11] that the

growth rate of fatigue cracks is dependent upon the stress intensity associated with the crack tip. The

power law relationship is of the form:

8|s

=A AK”

(2)



Through scaling of the Von Mises stress results for the NATX car Offset Vertical load case by the
ratio of 45/87, the highest estimated stress for the linear elastic analysis (originally 157 ksi) was
reduced to 81 ksi.

Tables 5 and 8, which summarize the Von Mises stress results for the Offset Vertical load
case, have been modified to reflect these estimated reductions in Von Mises stress for the NATX and
Trinity cars. No other tables, color contour plots, or captions for the Offset Vertical load case
stress results have been modified. The ratio of 45/87 may be applied to the other unmodified results
for the Offset Vertical load case to estimate the reduction in stress levels.

These new results for the Offset Vertical load case probably offer a better estimate of the
stresses typically induced by the Acoustic Emissions test. However, these results are still based on
estimates and verbal information. If a true assessment of the stresses induced by the Acoustic
Emissions test is required, additional analyses that are based on documented experimental data
should be run on both cars for this loading condition.

In summary, based on this analytical effort there is significant evidence that:

Both the NATX and Trinity tank cars showed that head braces significantly lower the
stresses in the tank shell area with head braces installed - which suggests that the
likelihood of fatigue cracking in these stub sill designs would be significantly reduced
compared with tank cars without head braces.

The head brace is less beneficial for reducing stresses in the Z-section lug area.

The likelihood of fatigue damage due to compression buff loads is not diminished by
the installation of a head brace.

The effects of a draft load on the structure should be the same as the buff load, except
opposite in sign. The draft load case was not run as a load case because we made the
assumption that the stresses from the draft load will be the same as those produced by
the buff load except opposite in sign. This should be verified experimentally or
analytically.


38

Table 8. Summary of Highest Stress Sites in the Trinity Car for each Load Case

Load Case Highest Von Potentially Critical Area Condition
Mises Stresses,
ksi
36 Rear Draft Lug Full, Head Brace
Compression
Buff 36 Rear Draft Lug Full, No Head Brace
Pai Z-Section Lug Area Full, No Head Brace
27 Z-Section Lug Area Full, Head Brace
21 Head Pad Full, No Head Brace
Upward 58 Head Pad Full, No Head Brace
Vertical r
27 Head Pad Radius Full, No Head Brace
26 Z-Section Head Pad Weld Full, No Head Brace
23 Tank Shell Full, No Head Brace
23 Head Brace Pad Full, Head Brace
Pure 20 Head Pad Full, No Head Brace
Torsi
orsion 8 Tank Shell Full, No Head Brace
Offset 45 Head Pad Full, No Head Brace
Vertical’ :
27 Z-Section Lug Area Full, No Head Brace
19 Z-Section Full, Head Brace
19 Z-Section Head Pad Weld and Full, No Head Brace
Z-Section Weld
17 Head Brace Pad Full, Head Brace
16 Head Pad Radius Full, No Head Brace
13 Head Pad Full, Head Brace

“Stress values for this case have been modified from original values - see Executive Summary.

critical sites within the component.

For the Trinity car it was assumed that the same potentially critical sites would apply as

previously identified for the NATX car. (These areas were shown earlier as darkened regions on
Figures 16 and 17.)



EXECUTIVE SUMMARY

A detailed stress analysis of two stub sill tank car designs was completed to gain an improved
understanding of the local stresses in these structures due to typical service loadings and to use this
information to better understand the fatigue cracking problems that have recurred in the past few years.
The primary area of concern in this investigation was the stub sill attachment region including the
welds on the underside of the tank car. Stress distributions due to ten specific reference loading
conditions were evaluated. The analytical results for two of these load cases were also compared with
experimental results developed at the Transportation Test Center (TTC) in Pueblo, CO.

The potentially critical stub sill locations are illustrated in Appendix A, where color plots of
the Von Mises stress contours are shown for each high stress location and loading combination.
Appendix B includes numerous local stress plots for each potentially critical location and Appendix C
shows detailed stress patterns resulting from the loading used as a part of the stub sill inspection
procedure.

One of the load cases examined for this study was the "Offset Vertical" case, which represents
the "Acoustic Emissions" test. The loading and boundary conditions given to Battelle for this case
were based on verbal descriptions and calculated estimates; no measurements or test data were made
available for the initial analyses. Several months later, after submission of the task final report, Dr.
Henry Fowler of Monsanto provided a better description of the loading and support conditions for the
Acoustic Emissions test. This information suggested that the boundary conditions and the load
magnitudes used in the initial model for the Offset Vertical (Acoustic Emissions test) load case led to
unrealistically high predicted stresses in the sill-to-tank interface area.

To assess the effect of these new boundary conditions on stress results, the Offset Vertical load
case was rerun with a reduced vertical load, a shortened offset (twist bar) and no restraint at the truck
pivot for the Trinity car with a full tank and no head brace. These new loads and boundary conditions
were estimates based on followup conversations with Dr. Fowler.

The peak Von Mises stress in the Sill-to-Tank-Pad interface area were reduced substantially
from 87 ksi to 45 ksi with these new boundary conditions applied. However, the distribution of
stresses in the most critical regions remained essentially unchanged, i.e., the highest stress sites
remained the same, with only the magnitude of the stresses changing. The reduced maximum
principal stresses in the sill-to-tank area on the side in tension was 25 ksi, and the minimum principal

stress in this same area on the side in compression (loaded side) was reduced in magnitude to -53 ksi.


32

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10.

LIST OF TABLES

Page
Stub Sill: Tank Car Load Cases. wise cine cree eieie rein oxene sive gies acne eueieue mine ele ernie © 4
Assumed Frequency and Severity of Field Loads for the Stub Sill Tank Car Fatigue
PNALY SIS) fo Siero ensue sienere, nce isteia, wien eseiel een, oven eon semen aieue ses diese eeeee Hed 228 21
Estimated Fatigue Properties From Reference [1] ...... 2... - 6c cece eee eee e eens 23
Summary of Maximum Von Mises Stresses for Potentially Critical Stub Sill Locations,
North American Tank Car; NATX 34081 Series ....... 2.60.6 cece eee eee ee eee 27
Summary of Highest Stress Sites in the NATX Car for each Load Case .. . 30
Summary of Orthogonal Stress Components in the NATX Car at Potentially Critical
Sites Identified in Appendix! Acseis 0 esses cre cere sieie niene wiele austere niece yee eere Riera mene 31
Summary of Maximum Von Mises Stresses for Potentially Critical Stub Sill Locations,
Trinity Car Class TK-S; ATSF 98600-94749 .... 0... cee eee ee ete ee eee eee 35
Summary of Highest Stress Sites in the Trinity Car for each Load Case ... 38
Summary of Orthogonal Stress Components in the Trinity Car at Potentially Critical
Sites Identified in Appendix A 40

Comparison of TTC Strain Gage Results with Battelle Finite Element Analysis Results .. 46

vii


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FIGURE B-31. TRINITY Z SECTION LUG AREA, LONGITUDINAL STRESS, COMPRESSION BUFF LOAD, FULL TANK,
WITH HEAD BRACE (FIRST VIEW); Maximum Stress


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21

specific gravity of only 0.54. If we had assumed another more dense lading, such as oil, the stress
results would have been proportionately higher in the load cases which included vertical components.
Since this was a linear, static analysis the horizontal inertial effects of the load’s mass (in a draft or
buff load case) were not directly solved for as part of the analysis. However, inertial effects were
included in the "static" load magnitudes for each particular load case, as defined by TTC[2]. The
effect of gravity was included in all load cases. The dead weight of the tank car load was simulated
by modifying (increasing) the density of tank elements.

2.4 Assumed Field Loading Spectra

Assumptions regarding the relationship between the modeled loads and typical field loads were
based on an earlier, related study by Battelle for the FRA[1]. These data are summarized in Table 2
for the compression buff and upward vertical load cases. The compression buff loading spectrum was
reasonably well defined based on AAR data developed under the FEEST program[4]. The upward
vertical loading spectrum was not as well defined. The estimates that are included in Table 2 are
based on the use of F Interlocking couplers; the limited data available[5] suggest the possibility of

Table 2. Assumed Frequency and Severity of Field Loads for the Stub Sill Tank Car Fatigue
Analysis
Loading Frequency Compression Buff Loading Upward Vertical
(Exceedances per Mile) (kips) (kips)

1 200 8

0.1 250 25

0.01 350 50

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offset vertical loading case was included to model the loading that has been applied to stub sill tank
cars at TTC as part of a nondestructive ("Acoustic Emissions") inspection test. The upward vertical

loading case was meant to simulate the significant vertical loads seen in service. As Table 1

illustrates, comparative analyses between head brace/no head brace and full tank/empty tank conditions

were also completed. Figures 3 through 6 show close up views of the stub sill area for both cars with

and without head braces.

Table 1. Stub Sill Tank Car Load Cases

LOAD CONFIGURATION
Compression Buff Full Tank Head Brace
Compression Buff Full Tank No Head Brace
Upward Vertical Full Tank Head Brace
Upward Vertical Full Tank No Head Brace
Pure Torsion Full Tank Head Brace
Pure Torsion Full Tank No Head Brace
Offset Vertical Full Tank Head Brace
Offset Vertical Full Tank No Head Brace
Offset Vertical Empty Tank Head Brace
Offset Vertical Empty Tank No Head Brace



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FIGURE B-33, TRINITY Z SECTION LUG AREA, VERTICAL STRESS, COMPRESSION BUFF LOAD, FULL TANK, WITH
HEAD BRACE (FIRST VIEW); Maximum Stress = 7.8 ksi, Minimum Stress


9
2.0 ANALYSIS PROCEDURE

A detailed finite element analysis was performed on two different stub sill tank car designs.
Sections 2.1 through 2.3 detail the finite element methodology that was used, assumed loading
configurations and boundary conditions, and key assumptions and areas of uncertainty. Sections 2.4
through 2.6 describe assumptions made conceming field service loads and the methodology used for
the fatigue crack initiation and crack growth estimates.

2.1 Mesh Generation and Modeling Assumptions

The SDRC I-DEAS program[3] was used to develop both of the models. The models
consisted of approximately 1000 linear, thin shell quadrilateral and triangular elements, 4000 linear
solid brick and wedge elements, 90 rigid elements, a few beam elements, and a total of about 7000
nodes. Figures 1 and 2 showed the overall car models and coordinate system orientation. Note that X
is the lateral (width) dimension, Y is the vertical (height) dimension, and Z is the fore-aft (length)
dimension.

The basic modeling approach was to develop a detailed solid model in the tank shell and draft
sill intersection areas surrounded by a coarse shell model of the rest of the car. This method provided
detailed stress results in the areas of concern and a good stiffness representation for each tank car in
areas where stress results were not required.

In each case, the coarse model was connected to the refined model using rigid elements. The
tigid elements were specified so that all displacement degrees of freedom were the same at the
intersection of the dissimilar (solid and shell) meshes. The rigid elements were also configured to
transmit all forces and moments at the interface.

Most welds in the coarse region were same-node connections since the shell elements that
were used have rotational degrees of freedom. Some weld connections were also made using rigid
elements. Welds in the refined region were modeled explicitly wherever possible. Solid wedge
elements were used for fillet welds, and solid brick elements were used for butt welds. Rigid elements

were used for some welded connections when mesh dissimilarities complicated the modeling.


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25

Based on prior studies[16] that showed the strong propensity for fatigue cracks to grow in Mode I
(opening mode due to stress excursions orthogonal to the plane of the crack), only the stress

components perpendicular to the assumed plane of cracking were considered.

3.0 EVALUATION OF CRACKING POTENTIAL AND CRITICALITY

In order to evaluate the potential for fatigue cracking at various sites within the stub sill
designs and to assess the likelihood of unstable cracking at these sites, a simplified fatigue and fracture

mechanics analysis was completed. This analysis was accomplished in four steps:

1) For the various load cases and tank car conditions the regions showing the
highest Von Mises stresses were identified.

2) Each of these regions were examined to identify the relative likelihood of
fatigue crack initiation (for an assumed mix of service loads described earlier).

3) The most probable sites for crack initiation (within the limits of the
assumptions required to complete the analysis) were examined to identify their
relationship to the regions of most common field cracking.

4) The principal stress components in each of these potentially critical sites were
examined to determine the relative likelihood of crack propagation and
subsequent fracture instability. The cracking sites with the greatest likelihood
of crack growth were deemed to be potentially dangerous (again within the
limits of the assumptions required to complete the analysis).

Details of the analysis are included in the following sections for both of the stub sill tank car

designs examined in this study.

3.1 North American Tank Car; NATX 34081 Series

The NATX tank car was examined first, and in the greatest detail. Lessons learned from this
analysis led to a somewhat more focussed examination of the Trinity car. Both analyses required
some basic assumptions regarding the relationship between the modeled loads and typical field service,

as well as assumptions concerning the fatigue resistance of the tank car materials.


10
2.1.1 Model Validation and Quality Assurance

The finite element models of both the NATX and the Trinity Car were checked for validity
and accuracy in several ways. The weight of the car components that were listed on the engineering
drawings were compared with the weight that the finite element program calculated.

Weld locations and plate thicknesses in the finite element model were independently checked
at Battelle by a knowledgeable person other than the person who built the finite element model. Plots
of the weld locations were routed through VNTSC to the Trinity Car Co. and to the North American
Car Co. for further confirmation. Sketches of loading and boundary conditions as understood by
Battelle were sent to VNTSC to confirm that these conditions were represented properly. Exaggerated
deformation plots were produced for each load case to confirm that the structure was reacting
realistically to the applied loadings.

Finite element analysis stress results along the bottom of the tank shell from the Compression
Buff load case were compared with a closed-form shell-theory analytical solution developed by
VNTSC. A comparison of finite element results with the output from the shell program is shown in
Figure 7. The results of the finite element analysis agreed with the VNTSC shell theory results within
about 14 percent near the load application point, and within 10 percent in areas away from the load
application point. The purpose of this comparison was not to achieve exact correlation; it was done to

provide a reasonability check for the finite element calculations.

2.2 Load Applications and Boundary Conditions

There were two different boundary conditions used, depending on load symmetry. The
"Quarter-Symmetric" load cases were the Compression Buff load and the Upward Vertical load. The
"Half-Symmetric" load cases were the Offset Vertical load cases (as used in the acoustic emission
inspections) with Full Tank and Empty Tank, and the Pure Torsion load case (simulating loading that
might occur in a tank car derailment). Figure 8 shows a quarter symmetric model, and Figure 9 shows
a half symmetric model.

There were a total of ten load cases which represented a combination of full tank/empty tank,
and head brace/no head brace configurations (as detailed earlier in Table 1). Figures 10 through 14

are illustrations of the loading conditions shown on the NATX car. The loading conditions were the


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LIST OF ABBREVIATIONS AND SYMBOLS

2N; Reversals to failure

A Crack growth rate coefficient, also cross-sectional area
a Crack length

AAR Association of American Railroads

AE Acoustic emission test

b Fatigue strength exponent

c Fatigue ductility exponent, also length in bending stress calculation
da/dN Crack growth rate

DOT Department of Transportation

FEA Finite element analysis

FEEST Freight Equipment Environmental Sampling Test
FRA Federal Railroad Administration

HAZ Heat affected zone

I Moment of inertia

K Cyclic strength coefficient

kips Thousands of pounds

LCF Longitudinal coupler force

M Moment

m Crack growth rate exponent
NATX North American Car Company
P Load

R Stress ratio

SG Strain gage

Smnax Maximum stress

Shain Minimum stress

Sy Ultimate strength

TTC Transportation Test Center

VCF Vertical coupler force

VNTSC Volpe National Transportation Systems Center, or Volpe Center
x Lateral (width) dimension

Y Vertical (height) dimension, also geometry dependent factor in stress intensity solution
Z Fore-aft (length) dimension
Greek Symbols

AK Stress intensity range

AS Stress range

Ag/2 Strain amplitude

Ecire Local circumferential strain

&; Fatigue ductility coefficient

fiong Local longitudinal strain

Hy Local strain

n Cyclic strain hardening exponent
Scire Circumferential stress

Oo; Fatigue strength coefficient

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30
Table 5. Summary of Highest Stress Sites in the NATX Car for each Load Case

Load Case Highest Von Potentially Critical Area Condition
Mises Stresses,
ksi
Compression 36 Transition Plate (End of Weld) Full, No Head Brace
Butt 29 Z-Section Lug Area Full, Head Brace
25 Transition Plate Radius Full, No Head Brace
Upward 126 Transition Plate (End of Weld) Full, No Head Brace
Vertical 72 Transition Plate Radius Full, No Head Brace
64 Transition Plate Tank Weld Full, No Head Brace
42 Z Section- Transition Plate Weld and | Full, No Head Brace
Z Section Weld
37 Z Section Lug Area Full, No Head Brace
Pure 21 Transition Plate (End of Weld) Full, No Head Brace
Torsion 20 Transition Plate Tank Weld Full, No Head Brace
16 Z Section- Transition Plate Weld and | Full, No Head Brace
Z Section Weld
Offset | 81 Transition Plate (End of Weld) Full, No Head Brace
Merdeal 68 Transition Plate Tank Weld Full, No Head Brace
50 Z Section- Transition Plate Weld and | Full, No Head Brace
Z Section Weld
46 Z Section Lug Area Full, No Head Brace
35 Tank Shell Full, No Head Brace
33 Transition Plate (End of Weld) Full, Head Brace
32 Z Section- Transition Plate Weld and | Full, Head Brace
Z Section Weld

“Stress values for this case have been modified from original values - see Executive Summary.

magnitude are considered, cracking across the transition plate would be most likely (due to draft
loads). However, large buff loads could also contribute to the growth of longitudinally oriented cracks
in the transition plate at the end of the weld.

Full NATX tank cars with head braces installed are also susceptible to the development of

dangerous service cracks, but the analysis suggests that the most likely site would be the Z-section lug


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